Fractional differential models for anomalous diffusion

In this study, we investigate three kinds of fractional differential models (distributed-order model, variable-order model and random-order model) for characterization of anomalous diffusion. The characteristics, physical advantages and potential applications of each model are highlighted. The numerical simulations also validate our analytical and comparison results. Furthermore, a generalized distributed-variable-order model and a more generalized distributed-variable-random-order model are proposed to combine the advantages of distributed-order model, variable-order model and random-order model.     

A Simplified Neuronal Model for the Instigation and Propagation of Cortical Spreading Depression

In this paper, we construct a simplified neuronal model that is capable of simulating the instigation of cortical spreading depression (CSD) and propagation of a CSD wave. Our model is a simplification and extension of a single neuron model proposed in the literature for studying the instigation of CSD. Using the simplified neuronal model, we construct a network of these simplified neurons. This network model shows that the propagation of a CSD wave occurs naturally after it is instigated electrically or chemically. Although the model is simple, the speed of the CSD wave predicted by our model is consistent with experimentally observed values. Finally, our model allows us to investigate the effects of specific ion channels on the spread of a CSD wave.     

The comparative analysis of prebiological evolution models

Several models of prebiological systems are described and analyzed. The following models are characterized: a quasispecies model, a hypercycle model, a syser model (the term "syser" is an abbreviation of SYstem of SElf-Reproduction), a stochastic corrector model, a model of the origin of a primordial genome through spontaneous symmetry breaking. The quasispecies model analyzes the Darwinian evolution of information chains; this evolution is similar to the evolution of RNA molecules. Rather general estimates of the speed and efficiency of evolutionary processes can be obtained in the framework of the quasispecies model. We briefly describe the method for obtaining these estimates and the corresponding results. The hypercycle model considers the interaction of RNA chains and enzymes. The syser model characterizes a rather general scheme of the self-reproducing system, which is similar to the self-reproducing systems of biological cells. Syser includes a polynucleotide sequence, a replication enzyme, a translation enzyme, and other enzymes; these macromolecules are located inside the protocell. The stochastic corrector model describes the process of using a relatively small number of molecules of competing and cooperating replicators in protocells. The model of the origin of a primordial genome through spontaneous symmetry breaking characterizes an interesting and important process of the appearance of genotypes in protocells. This model was proposed and investigated by Takeuchi, Hogeweg, and Kaneko in 2017; we call it further “the THK model.” The current article characterizes and compares all these models.     

包含液相扩散方程简化的锂离子电池电化学模型

锂离子电池的电化学模型对于电池特性分析和电池管理具有重要意义,但是准二维(P2D)模型复杂度太高,为了在保证模型精度的基础上尽量降低复杂度,本文提出了一种包含液相简化的P2D (LSP2D)模型,该模型首先基于电化学平均动力学将电池端电压化简成为仅耦合固相Li+浓度c_s和液相Li+浓度c_e的方程,然后进一步对表达c_s和c_e演化规律的偏微分方程进行抛物线近似化简,使得最终的模型由多项式组成.COMSOL仿真表明在放电倍率为1C时该模型与单粒子(SP)模型的估算精度和速度相当,但在放电倍率为3C时,该模型的估算时间比P2D模型减少了99.73%,与SP模型相当,估算精度相比SP模型有大幅度提升.     

The Odd Eight-Vertex Model

We consider a vertex model on the simple-quartic lattice defined by line graphs on the lattice for which there is always an odd number of lines incident at a vertex. This is the odd 8-vertex model which has eight possible vertex configurations. We establish that the odd 8-vertex model is equivalent to a staggered8-vertex model. Using this equivalence we deduce the solution of the odd8-vertex model when the weights satisfy a free-fermion condition. It is found that the free-fermion model exhibits no phase transitions in the regime of positive vertex weights. We also establish the complete equivalence of the free-fermion odd 8-vertex model with the free-fermion 8-vertex model solved by Fan and Wu. Our analysis leads to several Ising model representations of thefree-fermion model with pure 2-spin interactions.     

A dual model strategy to transfer multivariate calibration models for near-infrared spectral analysis

A dual-model method is proposed for correcting the calibration model. In the method, a primary calibration model is built using the spectra of a primary instrument and a correction model is established to describe the ratios between the predicted results from the spectra of different instruments. The prediction for the spectra of secondary instrument can be achieved by correcting the prediction of the primary model. A mathematical proof is described for the existence of the correction model, and the model is investigated using a near-infrared spectroscopic dataset of plant leaf samples measured on two instruments. The results show that a precise correction model is obtained and the model can be used to correct the predictions of the primary model. The correlation coefficients between the predicted and the reference ratios are above 0.9, and the prediction error after the correction is at the same level of the primary model.     

An asymmetric full velocity difference car-following model

This paper presents a car-following model that considers the asymmetric characteristic of the velocity differences of the vehicles in a traffic stream. The problems of the prevalent general force (GF) model and the full velocity difference (FVD) model were solved. Furthermore, the optimal velocity (OV) model, the GF model, and the FVD model are proved to be the special cases of the proposed asymmetric full velocity difference (AFVD) model. The mathematical model is presented, followed by simulation analysis which demonstrates the properties of the AFVD model.     

Application of the conditional source-term estimation model for turbulence–chemistry interactions in a premixed flame

Conditional Source-term Estimation (CSE) is a closure model for turbulence–chemistry interactions. This model uses the first-order CMC hypothesis to close the chemical reaction source terms. The conditional scalar field is estimated by solving an integral equation using inverse methods. It was originally developed and has been used extensively in non-premixed combustion. This work is the first application of this combustion model for a premixed flame. CSE is coupled with a Trajectory Generated Low-Dimensional Manifold (TGLDM) model for chemistry. The CSE-TGLDM combustion model is used in a RANS code to simulate a turbulent premixed Bunsen burner. Along with this combustion model, a similar model which relies on the flamelet assumption is also used for comparison. The results of these two approaches in the prediction of the velocity field, temperature and species mass fractions are compared together. Although the flamelet model is less computationally expensive, the CSE combustion model is more general and does not have the limiting assumption underlying the flamelet model.     

一种推广伊辛自旋模型的实空间重正化群理论

本文提出了一种推广的伊辛自旋模型。它包括了伊辛自旋模型、Schofield和Bowers提出的混合自旋模型以及一种特殊的格点稀释伊辛自旋模型作为特例。运用实空间重正化群得到了这个推广模型的相变流图和三个非平庸不动点(一个伊辛不动点,一个三相不动点和一个一级相变不动点)。结果表明:混合自旋模型和伊辛模型属于同一普适类。证实了Schofield和Bowers通过直接对混合自旋模型临界指数的计算所做的结论。 关键词：     

相变过程的格子Boltzmann方法模拟

应用Shan提出的伪势多相模型替代R-K着色模型,建立一种新的描述气液相变过程的格子Boltzmann理论模型,模拟蒸发(高密度转化为低密度)过程.改进了计算效率,且得到较好的计算结果.同时应用该模型从孔隙尺度模拟了多孔介质中的相变现象,验证了该模型模拟复杂相变问题的可行性.     

The dynamic evolutions of the generalized Hobbit model and structure formation

In this paper a more general phenomenological model is proposed on the basis of the Hobbit model in Cardone et al. (Phys Rev D 69:083517, 2004). The main purpose of constructing our model is to make this model can not only mimic the ΛCDM model, but also describe a four-phase smooth transition of the universe, namely the inflationary phase, a radiation-dominated phase, a matter-dominated phase and a de Sitter-like phase. In order to check whether this model is a viable one, the evolutions of the universe are respectively discussed in the two cases, and the possible physical interpretations for this model are also respectively shown by using the scalar fields. Finally, the structure formations in our model are simply discussed for the both cases, and the results given by us reconfirm that our model can be regarded as a fit to the ΛCDM model, if we choose the proper conditions.     

Meta-Tree Random Forest: Probabilistic Data-Generative Model and Bayes Optimal Prediction

This paper deals with a prediction problem of a new targeting variable corresponding to a new explanatory variable given a training dataset. To predict the targeting variable, we consider a model tree, which is used to represent a conditional probabilistic structure of a targeting variable given an explanatory variable, and discuss statistical optimality for prediction based on the Bayes decision theory. The optimal prediction based on the Bayes decision theory is given by weighting all the model trees in the model tree candidate set, where the model tree candidate set is a set of model trees in which the true model tree is assumed to be included. Because the number of all the model trees in the model tree candidate set increases exponentially according to the maximum depth of model trees, the computational complexity of weighting them increases exponentially according to the maximum depth of model trees. To solve this issue, we introduce a notion of meta-tree and propose an algorithm called MTRF (Meta-Tree Random Forest) by using multiple meta-trees. Theoretical and experimental analyses of the MTRF show the superiority of the MTRF to previous decision tree-based algorithms.     

Analytical model for nanoscale viscoelastic properties characterization using dynamic nanoindentation

In the last few decades, nanoindentation has gained widespread acceptance as a technique for materials properties characterization at micron and submicron length scales. Accurate and precise characterization of material properties with a nanoindenter is critically dependent on the ability to correctly model the response of the test equipment in contact with the material. In dynamic nanoindention analysis, a simple Kelvin–Voigt model is commonly used to capture the viscoelastic response. However, this model oversimplifies the response of real viscoelastic materials such as polymers. A model is developed that captures the dynamic nanoindentation response of a viscoelastic material. Indenter tip-sample contact forces are modelled using a generalized Maxwell model. The results on a silicon elastomer were analysed using conventional two element Kelvin–Voigt model and contrasted to analysis done using the Maxwell model. The results show that conventional Kelvin–Voigt model overestimates the storage modulus of the silicone elastomer by ~30%. Maxwell model represents a significant improvement in capturing the viscoelastic material behaviour over the Voigt model.     

The phase diagram of the 2D Ising model with anisotropic next-nearest-neighbor and four-spin interactions

In the present paper, the two-dimensional Ising model with anisotropic nearest-neighbor, next-nearest-neighbor and four-spin interactions has been studied. The ground states and energy of the model have been obtained. The model is equivalent to an eight-vertex model on its dual lattice. In some special cases, the model can be solved exactly as a zero-field eight-vertex model or a free-fermion model. Explicit phase diagrams are obtained exactly.     

Effective two-mode description of a few ultra-cold bosons in a double-well potential

We present a construction of an improved two-mode model for modeling the dynamics of interacting ultra-cold bosons confined in a one-dimensional double well trap. Unlike in the typically used two-mode model based on the lowest single-particle eigenstates of the external potential, the improved model uses a basis of properly chosen effective wave functions originating in the many-body model. Accuracy of the improved model is examined and it is shown that within a certain limit of inter-particle interaction strength, the model recovers an exact evolution of the wells' populations much more closely than the traditional two-mode model.     

Cellular automaton model considering headway-distance effect

This paper presents a cellular automaton model for single-lane traffic flow. On the basis of the Nagel-Schreckenberg （NS） model, it further considers the effect of headway-distance between two successive cars on the randomization of the latter one. In numerical simulations, this model shows the following characteristics. （1） With a simple structure, this model succeeds in reproducing the hysteresis effect, which is absent in the NS model. （2） Compared with the slow-tostart models, this model exhibits a local fundamental diagram which is more consistent to empirical observations. （3） This model has much higher efficiency in dissolving congestions compared with the so-called NS model with velocitydependent randomization （VDR model）. （4） This model is more robust when facing traffic obstructions. It can resist much longer shock times and has much shorter relaxation times on the other hand. To summarize, compared with the existing models, this model is quite simple in structure, but has good characteristics.     

用于脉冲等离子体推力器烧蚀过程仿真的新型机电模型

用于脉冲等离子体推力器(PPT)工作过程仿真的一维机电模型, 具有模型简单、计算周期短等优点, 在PPT设计过程中得到了广泛应用. 本文针对机电模型假设工质烧蚀质量为常数和不考虑烧蚀过程这一局限, 提出了一种采用Teflon一维烧蚀模型计算工质烧蚀质量的改进模型, 并以LES-6 PPT为研究对象进行了仿真. 通过与LES-6 PPT实验数据进行对比, 仿真结果与实验数据符合, 充分验证了模型的可靠性. 此模型能够对Teflon工质在PPT工作过程中的温度变化和烧蚀过程进行仿真, 弥补了机电模型忽略烧蚀过程对仿真结果所造成的影响, 同时, 此模型依然保持了机电模型简单易于实现的优点, 对于脉冲等离子体推力器的设计具有重要意义. 关键词： 脉冲等离子体推力器 机电模型 烧蚀模型 数值仿真     

Modelling dynamic behaviour and noise generation in gear pumps: Procedure and validation

The paper presents a methodology for noise and vibration analysis of gear pumps and its application to an external gear pump for automotive applications. The methodology addresses the use of a combined numerical model and experimental analyses. The combined model includes a lumped-parameter model, a finite-element model and a boundary-element model. The lumped-parameter (LP) model regards the interior parts of the pump (bearing blocks and gears loaded by the pressure distribution and the driving torque), the finite element (FE) model regards the external parts of the pump (casing and end plates), while the boundary element (BE) model enables the estimation of the emitted noise in operational conditions. Based on experimental evidences, attention has been devoted to the modelling of the pump lubricant oil: the fluid–structure interaction between the oil and pump casing was taken into account. In the case of gear pumps all these important effects have to be considered in the same model in order to take their interactions into account. The model has been assessed using experiments: the experimental accelerations and acoustic pressure measured in operational conditions have been compared with the simulated data coming from the combined LP/FE/BE model. The combined model can be considered a very useful tool for design optimisation.     

基于守恒高阶模型的动态交通分配建模与仿真

针对路网中的动态交通分配问题，采用高阶守恒模型（CHO）进行建模与数值研究，并推广高阶守恒模型二进二出路口的Riemann问题；同时将高阶守恒模型与动态网络加载（DNL）模型相结合，通过变分不等式对动态网络加载模型进行分析.数值模拟采用一阶有限体积法求解高阶守恒模型，同时采用梯度下降方法迭代求解动态网络加载模型的变分不等式问题，最终以动态用户最优条件为目标实现分配均衡.数值结果表明CHO模型与DNL模型结合解决动态交通分配问题是可行的，对传统模型的研究有一定的指导意义.     

An Efficient Three-Dimensional Coupled Normal Mode Model and Its Application to Internal Solitary Wave Problems

We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forward scattering dominates. At the same time, this model provides an efficiency gain of an order of magnitude or more over two-way coupled-mode models. This model can be applied to three-dimensional range-dependent problems with a slowly varying bathymetry or internal waves. A numerical example of the latter is demonstrated in this work. Comparisons of both accuracy and efficiency between the present model and a benchmark model are also provided.